Simplify the following expression and state the condition under which the simplification is valid: $q = \dfrac{y^2 - 3y}{y^2 - 6y + 9}$
Answer: First factor the expressions in the numerator and denominator. $ \dfrac{y^2 - 3y}{y^2 - 6y + 9} = \dfrac{(y)(y - 3)}{(y - 3)(y - 3)} $ Notice that the term $(y - 3)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(y - 3)$ gives: $q = \dfrac{y}{y - 3}$ Since we divided by $(y - 3)$, $y \neq 3$. $q = \dfrac{y}{y - 3}; \space y \neq 3$